scholarly journals Graph properties checkable in linear time in the number of vertices

2004 ◽  
Vol 68 (3) ◽  
pp. 546-597 ◽  
Author(s):  
Etienne Grandjean ◽  
Frédéric Olive
Keyword(s):  
2009 ◽  
Vol 20 (06) ◽  
pp. 1005-1023 ◽  
Author(s):  
PAWEŁ BATURO ◽  
MARCIN PIATKOWSKI ◽  
WOJCIECH RYTTER

The class of finite Sturmian words consists of words having particularly simple compressed representation, which is a generalization of the Fibonacci recurrence for Fibonacci words. The subword graphs of these words (especially their compacted versions) have a very special regular structure. In this paper we investigate this structure in more detail than in previous papers and show how several syntactical properties of Sturmian words follow from their graph properties. Consequently simple alternative graph-based proofs of several known facts are presented. The very special structure of subword graphs leads also to special easy algorithms computing some parameters of Sturmian words: the number of subwords, the critical factorization point, lexicographically maximal suffixes, occurrences of subwords of a fixed length, and right special factors. These algorithms work in linear time with respect to n, the size of the compressed representation of the standard word, though the words themselves can be of exponential size with respect to n. Some of the computed parameters can be also of exponential size, however we provide their linear size compressed representations. We introduce also a new concept related to standard words: Ostrowski automata.


2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Yilun Shang

Stochastic multiagent systems have attracted much attention during the past few decades. This paper concerns the continuous-time consensus of a network of agents under directed switching communication topologies governed by a time-homogeneous Markovian process. The agent dynamics are described by linear time-invariant systems, with random noises as well as time-varying delays. Two types of network-induced delays are considered, namely, delays affecting only the output of the agents’ neighbors and delays affecting both the agents’ own output and the output of their neighbors. We present necessary and sufficient consensus conditions for these two classes of multiagent systems, respectively. The design method of consensus gains allows for decoupling the design problem from the graph properties. Numerical simulations are implemented to test the effectiveness of our obtained results as well as the tightness of necessary/sufficient conditions.


1995 ◽  
Vol 34 (05) ◽  
pp. 475-488
Author(s):  
B. Seroussi ◽  
J. F. Boisvieux ◽  
V. Morice

Abstract:The monitoring and treatment of patients in a care unit is a complex task in which even the most experienced clinicians can make errors. A hemato-oncology department in which patients undergo chemotherapy asked for a computerized system able to provide intelligent and continuous support in this task. One issue in building such a system is the definition of a control architecture able to manage, in real time, a treatment plan containing prescriptions and protocols in which temporal constraints are expressed in various ways, that is, which supervises the treatment, including controlling the timely execution of prescriptions and suggesting modifications to the plan according to the patient’s evolving condition. The system to solve these issues, called SEPIA, has to manage the dynamic, processes involved in patient care. Its role is to generate, in real time, commands for the patient’s care (execution of tests, administration of drugs) from a plan, and to monitor the patient’s state so that it may propose actions updating the plan. The necessity of an explicit time representation is shown. We propose using a linear time structure towards the past, with precise and absolute dates, open towards the future, and with imprecise and relative dates. Temporal relative scales are introduced to facilitate knowledge representation and access.


Sign in / Sign up

Export Citation Format

Share Document